Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Tan, Xinsheng; Zhang, Dan‐Wei; Yang, Zhen; Chu, Ji; Zhu, Yan-Qing; Li, Danyu; Yang, Xiaopei; Lan, Dong; Han, Zhikun; Li, Zhiyuan; Dong, Yuqian; Yu, Haifeng; Yan, Hui; Zhu, Shining; Yu, Yang

doi:10.1103/physrevlett.122.210401

Cited by 120 publications

(86 citation statements)

References 49 publications

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“…The absence of Berry curvature indicates that such topological defects cannot be signaled through standard topological responses [8]. In the following, we investigate the non-vanishing quantum metric associated with the band structure; we show that this observable quantity, which can be extracted from dissipative responses [47][48][49], can indeed provide a direct signature for topological nodal rings. In general, the three-dimensional quantum metric related to nodal lines is rather complicated.…”

Section: ]mentioning

confidence: 99%

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Salerno

Goldman

Palumbo

2020

Phys. Rev. Research

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Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual topological defects that are analogous to extended monopoles. In this work, we describe a scheme by which nodal rings and nodal spheres can be realized in synthetic quantum matter through well-defined periodic-driving protocols. As a central result of our work, we characterize these nodal defects through the quantum metric, which is a gauge-invariant quantity associated with the geometry of quantum states. In the case of nodal rings, where the Berry curvature and conventional topological responses are absent, we show that the quantum metric provides an observable signature for these extended topological defects. Besides, we demonstrate that quantum-metric measurements could be exploited to directly detect the topological charge associated with a nodal sphere. We discuss possible experimental implementations of Floquet nodal defects in few-level atomic systems, paving the way for the exploration of Floquet extended monopoles in quantum matter. arXiv:1912.00930v1 [cond-mat.mes-hall]

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Section: ]mentioning

confidence: 99%

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Salerno

Goldman

Palumbo

2020

Phys. Rev. Research

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“…Recently, experimental measurements of the quantum metric tensor and the full quantum geometric tensor in two‐level systems described by Equation were reported in refs. [] and [], respectively (see also ref. []).…”

Section: Illustrative Examplesmentioning

confidence: 99%

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Alvarez‐Jimenez¹,

González²,

Gutiérrez‐Ruiz³

et al. 2019

Annalen der Physik

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The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin‐half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.

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“…In fact, local topological properties can also be revealed by the quantized spectroscopic response under (nonadiabatic) circular drive [38,39], which has already been successfully carried out in Floquet states of ultracold fermionic atoms under time-dependent drive [40,41]. Similarly, a nontrivial (Floquet) topology was achieved in superconducting qubits [42,43] generated by custom-built engineered time-dependent drives.…”

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confidence: 99%

Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter

et al. 2020

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Quantization effects due to topological invariants such as Chern numbers have become very relevant in many systems, yet key quantities such as the quantum geometric tensor providing local information about quantum states remain experimentally difficult to access. Recently, it has been shown that multiterminal Josephson junctions constitute an ideal platform to synthesize topological systems in a controlled manner. We theoretically study properties of Andreev states in topological Josephson matter and demonstrate that the quantum geometric tensor of Andreev states can be extracted by synthetically polarized microwaves. The oscillator strength of the absorption rates provides direct evidence of topological quantum properties of the Andreev states.

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Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Cited by 120 publications

References 49 publications

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter

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